$K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 9x - 6$ and $ KL = 4x + 14$ Find $JL$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {9x - 6} = {4x + 14}$ Solve for $x$ $ 5x = 20$ $ x = 4$ Substitute $4$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 9({4}) - 6$ $ KL = 4({4}) + 14$ $ JK = 36 - 6$ $ KL = 16 + 14$ $ JK = 30$ $ KL = 30$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {30} + {30}$ $ JL = 60$